English

not defined

no text concepts found

Math 1303 Review for Test #2 Linear: Equations/Inequalities/Systems/Programming 1. Page 11 (17 – 24; 25 – 28) Solve each inequality. Sketch the solution graph on a number line and write the solution in interval notation. a. 2(2x + 3) < 6(x – 2) + 10 b. −8 < 3x – 5 < 7 2. See notes and quizzes. Use the “sign chart” method for determining the solution to the inequality. Graph the solution on a number line and write the solution in interval notation. a. x2 – 13x + 36 > 0 x 2 7 x 12 < 0 x5 b. 3. See notes and quizzes. Write the equation of each line described below: a. Tangent to the circle (whose equation is shown below) at the point (−2, −1). x2 + y2 – 4x – 6y – 19 = 0 4-5. Page 179 (17 – 26); Page 191 (45 – 49); Page 202 (39 – 41) Solve each linear system (use whichever method your prefer (examples are of each method) a. Graph: 2 x 3 y 12 x 2y 6 b. Substitution: c. Linear combination (addition): 3x y 1 7 x 2 y 1 2 x 4 y 8 3 x 2 y 4 d. Gauss-Jordan (use calculator---show appropriate work): 3 x 5 y 9 2 x 3 y 5 3x 2 y 8 z 9 2 x 2 y z 3 x 2 y 3z 8 6. Page 180 (57 (ABC), 58 (ABC), 61A, 62A, 63A, 64A, 71); Page 203 (65A, 66A) a. We are interested in analyzing the sale of cherries each day in a particular town. An analyst arrives at the following price-demand and price-supply models: Supply: p = −0.2q + 4 Demand: p = 0.07q + 0.76 p = price (dollars) q = # pounds (1000’s) How many pounds of cherries can be sold if the price is $2 per pound? How many pounds of cherries can the supplier provide is the price is $2 per pound? Find the equilibrium price and quantity. b. Set up a system of equations and then solve: Michael Perez has a total of $2,000 on deposit with two savings institutions. One pays interest at the rate of 6% per year, whereas the other pays interest at the rate of 8% per year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposit in each account? 7. Page 256 (1 – 10; 33-37) Sketch the graph of the linear inequality: 4x – 5y > 40 8. Page 263 (13 – 22) Sketch the graph of the linear system shown below. Then find all corner points. Determine whether the solution region is bounded or unbounded. x > 2 5x + 3y > 30 x – 3y > 0 9. Page 273 (9 – 16) Solve the linear programming problem: Maximize P = 4x + 2y subject to x+y < 8 2x + y < 10 x > 0 y > 0 10. Page 275 (31A, 32A 33A, 34AB) Set up a linear programming problem to solve the following. Then use the graphing method to find the needed value. National Business Machines manufactures two models of fax machines: A and B. Each model A costs $100 to make, and each model B costs $150. The profits are $30 for each model A and $40 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $330,000 per month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profit? What is the optimal profit?